Channel-Constrained Information Scheduling for Quantum Diffusion
Abstract
Information-based diffusion schedules organize the reverse problem by prescribing how much source information remains after each forward step. For mixed-state quantum diffusion, density-level targets need not correspond to trajectories reachable from the current realization. We introduce \emph{channel-constrained information scheduling}: each step optimizes over source-blind pure-state refinements reachable from the current state-resolved record through the prescribed channel. This defines a channel-constrained information clock Vξ, whose inverse selects the least-corrupting step that reaches a target information level. Recursive inversion constructs a realizable equal-information schedule minimizing the worst source-information burden in Bayes reverse prediction. We establish attainment, continuity, monotonicity, convexity, finite support, and exact primal/dual formulations for Vξ. We further give a sharp structural characterization: binary-qubit depolarizing trajectories attain the density-level Belavkin--Staszewski envelope, whereas every d≥3 admits binary noncommuting families with a strict static--dynamic separation. Qutrit experiments show that the proposed scheduler nearly equalizes the realized multi-step burden, and learned reverse predictors recover the predicted allocation.
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BibTeX
@misc{qian2026channelconstrained,
title = {{Channel-Constrained Information Scheduling for Quantum Diffusion}},
author = {Qipeng Qian and Yuntao Qian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26273},
eprint = {2609.26273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26273},
}
RIS
TY - UNPB
TI - Channel-Constrained Information Scheduling for Quantum Diffusion
AU - Qipeng Qian
AU - Yuntao Qian
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26273
UR - https://arxiv.org/abs/2609.26273
AB - Information-based diffusion schedules organize the reverse problem by prescribing how much source information remains after each forward step. For mixed-state quantum diffusion, density-level targets need not correspond to trajectories reachable from the current realization. We introduce \emph{channel-constrained information scheduling}: each step optimizes over source-blind pure-state refinements reachable from the current state-resolved record through the prescribed channel. This defines a channel-constrained information clock V_ξ, whose inverse selects the least-corrupting step that reaches a target information level. Recursive inversion constructs a realizable equal-information schedule minimizing the worst source-information burden in Bayes reverse prediction. We establish attainment, continuity, monotonicity, convexity, finite support, and exact primal/dual formulations for V_ξ. We further give a sharp structural characterization: binary-qubit depolarizing trajectories attain the density-level Belavkin--Staszewski envelope, whereas every d≥3 admits binary noncommuting families with a strict static--dynamic separation. Qutrit experiments show that the proposed scheduler nearly equalizes the realized multi-step burden, and learned reverse predictors recover the predicted allocation.
ER -